1.18: Attributive and Predicate Position
Module 15
© 2021 Philip S. Peek, CC BY 4.0 https://doi.org/ 10.11647/OBP.0264. 18
Word Order
Greek creates meaning through prepositional phrases and through endings. Word order also matters. Attributive position creates meaning by placing the article and the attribute in a specific sequence. As you read, pay attention to the arrangement of words, noticing why word order matters in Greek.
Attributive Position
Attributive position tells us that a noun is to be translated with other words. Consider the phrase the woman in the road . Since the woman referred to is the person standing in the road, Greek may place the words in the road into attributive position with the noun woman.
Consider another phrase, the white stripes . In this example, the noun stripes is described by the adjective white and so Greek can place the adjective, white , into attributive position with the noun, stripes .
In the examples below the attributes ὑπὸ λίθῳ under a rock and καλό ς good are in bold; underlined are the articles and nouns, σκορπίος , σκορπίου ὁ scorpion and ὄνειρος , ὀνείρου ὁ dream . The general rule for attributive position is that the article will directly precede the attribute. Three possibilities exist.
1. article attribute noun :
- the scorpion under a rock
- the good dream
2. article noun article attribute :
- the scorpion under a rock
- the good dream
3. noun article attribute :
- the scorpion under a rock
- the good dream
Note that in all of the above examples, the article directly precedes the attribute.
Other Possibilities
Greek uses attributive position to tell you what words are to be translated together to create a phrase. When no article is present, consider these four examples,
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Example 1: |
ὑπ ’ ἐλάταις γυναῖκες |
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option 1: |
women under pine trees |
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option 2: |
women are under pine trees. |
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Example 2: |
ἓν μόνον ἀ γαθόν |
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option 1: |
only one good |
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option 2: |
there is only one good. |
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Example 3: |
βίος βραχύς |
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option 1: |
a short life |
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option 2: |
life is short. |
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Example 4: |
οὐδὲν κακό ν |
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option 1: |
nothing evil |
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option 2: |
there is nothing evil. |
Predicate Position
If the words are not in attributive position and an article is present, consider these two examples,
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Example 1: |
ὁ βίος βραχύς . |
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option 1: |
life is short. |
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Example 2: |
ἐν τῷ κινδύνῳ ὁ ἄνθρωπος |
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option 1: |
the man is in danger. |
This arrangement of words with the article present is called predicate position .
Practice with Attributive Position. Write out the following in all forms of attributive position. Check your answers with those in the Answer Key .
- the harsh road ( ἡ ὁ δός ; χαλεπή )
- the wise word ( ὁ λόγος ; σοφός )
- the noble soul ( ἡ ψυχ ή ; ἀγαθή )
Practice with Predicate Position. Write out the following in all forms of predicate position. Check your answers with those in the Answer Key .
- the road is harsh ( ἡ ὁδός ; χαλεπή )
- the word is wise ( ὁ λόγος ; σοφός )
- the soul is noble ( ἡ ψυχή ; ἀγαθ ή )
Ancient Greek Thought and Living Well
During the Archaic Age (799–480 BCE) and after, Greeks in the various city-states of Hellas were becoming increasingly aware of their rationale for doing things. They recognized custom, usage, and tradition as the reasons behind much of what they did and many of the beliefs and values they held. Thus they began to look for a better way to live well and a better authority for their beliefs, conventions, institutions, and values. One place they looked was nature and soon saw that, in nature, birth and wealth were irrelevant. Another place they looked was to logic and reason. Intellectuals, including philosophers and sophists, engaged in these inquiries.
Philosophical inquiry predates sophism, the discipline of the sophists. Philosophers asked if the universe had a beginning, how it began, and what its elements were. They saw the world as something ordered and rational and sought to explain as much as possible in terms as little as possible, i.e., via theories. These intellectuals were often highly skilled mathematicians.
Sophism can be traced at least back to the early 6th century when philosophers—from the Greek adjective φιλόσοφος lover of wisdom —were intent on explaining the universe and all its contents by means of science rather than religion. The loan word sophism comes from the Greek adjective, σοφ ός , σοφή , σοφόν , clever, skilled, wise . Sophists were mainly itinerant teachers, travelling from city to city, teaching for a fee various subjects, including physics, astronomy, mathematics, and the art of rhetoric. They promised their pupils material success through bettering themselves by education. Sophists were viewed by some as having a corrupting influence on the young by teaching them atheism, scientific inquiry, rhetoric (making the lesser argument the stronger), and a new relativistic morality.
In the below there is a list of some prominent Greek intellectuals. In the Practice Translating that follows, you will read fragments written by Thales, Herakleitos, Aiskhylos, Euripides, Antiphon, Sokrates, and Aristoteles.
Thales of Miletos, Θαλ ῆς ὁ Μιλήσιος , c. 624 BCE. Thales was a pre-Socratic philosopher who predicted an eclipse of the sun in 585 BCE and argued that the universe’s prime element was water . Two of Thales’ writings are found below in the Practice Translating .
Anaximandros of Miletos, Ἀναξίμανδρος ὁ Μιλήσιος , c. 610–546 BCE. Anaximandros was a pre-Socratic philosopher who put forth the theory that the infinite was the universe’s origin.
Anaximenes of Miletos, Ἀναξιμένης ὁ Μιλήσιος , c. 586–526 BCE. Anaximenes was a pre-Socratic philosopher who proposed air as the universe’s prime substance.
Pythagoras of Samos, Πῡθαγόρᾱς ὁ Σάμιος , c. 570–495 BCE. Pythagoras was a pre-Socratic philosopher who argued that the soul was immortal and after its death was reborn into another body, either man, animal, or plant, through a process called metempsychosis, μετεμψύχωσις . The only end to this cycle was to attain purity of intellect and soul.
Xenophanes of Kolophon, Ξενοφάνης ὁ Κολοφώνιος , c. 570–478 BC Ε . Xenophanes was a pre-Socratic philosopher who criticized Hesiod and Homer, arguing that their explanation of divine and human affairs was incorrect. He also criticized the adulation of athletes because wise men were much more important to society than some champion boxer. Finally, he asserted that the gods were not anthropomorphic but that there was one god who was moral and motionless, all-knowing and all-powerful.
Herakleitos (Heraclitus) of Ephesos, Ἡράκλειτος ὁ Ἐφέσιος , c. 535–475 BCE. Herakleitos was a pre-Socratic philosopher who argued that the universe’s prime substance was fire, which all things contained within them, that the universe had always existed, and that all is in flux for one can never step into the same river twice. Three quotes by him are found below in the Practice Translating .
Aiskhylos (Aeschylus) of Athens, Αἰσχύλος ὁ Ἀθηνα ῖος , c. 525–456 BCE. Aiskhylos wrote satyr plays and tragedies. He composed about ninety plays, of which seven survive. Many fragments from his other plays are found quoted by other later authors or on Egyptian papyrus scraps. Aristoteles writes that Aiskhylos expanded the number of characters in the theatre and allowed them to interact with each other instead of only with the chorus. One of his plays, Prometheus Bound , may have been written by his son, Euphorion. Another of his plays, The Persians , is the only extant tragedy concerning contemporary events that survives. One quote by him is found below in the Practice Translating .
Parmenides of Elea, Παρμενίδης ὁ Ἐλεάτης , c. 500 BCE. Parmenides was a pre-Socratic philosopher who reasoned that the earth was a sphere and that sense perception was illusory. Thus the only way to truth was through logic.
Anaxagoras of Klazomenai, Ἀναξαγόρας , Κλαζομεναί , c. 500–428 BCE. Anaxagoras was a pre-Socratic philosopher and a good friend of the Athenian statesman Perikles. Anaxagoras spent much of his time in the cultural center of his day, Athens. He declared that the sun was a stone and not a god. The Athenians may have brought him to court and had him exiled on charges of impiety and pro-Persian sympathies. It is uncertain if the charges were real, political, or fabricated by later biographers.
Sophokles (Sophocles) of Athens, Σοφοκλῆς ὁ Ἀθηναῖ ος , c. 497–406 BCE. Sophokles wrote satyr plays and tragedies. He composed over 120 plays and seven have survived, the most famous being Oidipous Tyrannos ( Oidipous Rex ) and Antigone . He is said to have won twenty-four of the thirty competitions he entered.
Empedokles of Akragas, Ἐμπεδοκλῆς , Ἀκράγας , Σικελία , c. 494–434 BCE. Empedokles was a pre-Socratic philosopher, who contended that the senses were routes to knowledge and that the universe was made up of the following four substances: earth, air, fire, and water.
Protagoras of Abdera, Thrace, Πρωταγόρας , Ἄβδηρα , Θρᾴκη , c. 490–420 BCE. Protagoras was a pre-Socratic philosopher. In his dialogue Protagoras , Plato writes that Protagoras invented the professional sophist. Protagoras argued that it did not matter whether the gods existed—he was an agnostic—that there were two sides to every question, each opposed to the other; that the soul was nothing apart from the senses; that everything is true; that all values were relative; and that man is the “measure of all things, of things that are that they are, and of things that are not that they are not.” For these views it is said that the Athenians expelled him from their city and burnt his works in the marketplace (Diogenes Laertius 9. 51–52).
Gorgias of Leontini, Γοργίας , Λεοντῖ νοι , c. 483–376 BCE. Gorgias was a sophist, who specialized in teaching the art of rhetoric.
Antiphon of Rhamnos, Ἀντιφῶν ὁ Ῥαμνούσιος , c. 480–411 BCE. Antiphon was an orator, engaged in 5th-century Athenian political and intellectual life. One quote by him is found below in the Practice Translating .
Euripides of Athens, Εὐριπίδης ὁ Ἀθηναῖος , c. 480–406 BCE. An innovator who did not gain wide acceptance until after his death, Euripides wrote satyr plays and tragedies. He introduced comedy into tragedy and presented the heroes and heroines of his plays as everyday people. He was a proponent of the new music, which broke with tradition and is a feature of his work that shocked some of his contemporaries. In several plays ( Helen , Ion , Iphigeneia in Tauris ), he created tragicomic plots that foreshadowed the so-called New Comedy. Four quotes by him are found below in the Practice Translating .
Sokrates (Socrates) of Athens, Σωκρᾰ ́της ὁ Ἀθηναῖος , c. 469–399 BCE. Sokrates was an Athenian stonemason and carver and very poor. He was accused of being a sophist and was loved by some and hated by many of the Athenian people. Early in life Sokrates was intrigued by scientific speculation. He soon grew skeptical of it and turned his attention to inquiring into the right conduct of life. Two quotes by him are found below in the Practice Translating .
Demokritos (Democritus) of Abdera , Thrace, Δημόκριτος , Ἄβδηρα , Θρᾴκη , c. 460–370 BCE. Demokritos was a pre-Socratic philosopher, who proposed that all things were composed of atoms and void. Atoms were the smallest building blocks of the universe and void allowed motion to occur. His theory was later popularized by Epikouros and then expounded by the Roman poet and philosopher Lucretius. Six quotes by him are found below in the Practice Translating .
Hippokrates (Hippocrates) of Kos, Ἱπποκράτης ὁ Κῷος , c. 460–370 BC. Hippokrates was a physician, who made outstanding contributions to the field of medicine. Founder of the Hippocratic School of Medicine, he established medicine as a discipline and profession. He is credited with writing the Hippocratic Oath, a code of ethics still in use today.
Thrasymakhos of Khalkedon, Θρασύμαχος , Χαλκηδών , c. 459–400 BCE. Thrasymakhos was a sophist, who taught that justice is the interest of the stronger, i.e., that “might makes right.” He is best known as a character in Plato’s Republic .
Aristophanes of Athens, Ἀριστοφάνης ὁ Ἀθηνα ῖος , c. 446–c. 386 BCE. Aristophanes wrote comic plays. Of forty or so plays, eleven have survived and represent a genre of comic drama referred to as Old Comedy.
Platon (Plato) of Athens, Πλάτων ὁ Ἀθηναῖος , c. 428–424 BCE. Plato was a student of Sokrates and a philosopher. Best known for his theory of forms and highly influential in his own day, Plato’s works continue to be read and studied.
Diogenes the Cynic of Sinope, Διογένης ὁ Κυνικός , Σινώπη , c. 412–323 BCE. Diogenes was a philosopher and founder of the Cynic school of philosophy. He believed in moral action rather than in theory. He lived simply and frugally, looking to nature as a guide to living well and authentically, declaring himself a citizen of the world.
Aristoteles (Aristotle) of Stageira, Ἀριστοτέλης , Στάγειρα , c. 384–322 BCE. Aristoteles was a student of Plato and a philosopher. He founded the peripatetic school of philosophy and wrote on many subjects, including aesthetics, biology, economics, ethics, government, linguistics, logic, metaphysics, music, physics, poetry, politics, psychology, rhetoric, theater, and zoology. Aristotle’s works continue to be read and studied. One of his quotes is found below in the Practice Translating .
Menandros (Menander) of Athens, Μένανδρος ὁ Ἀθηναῖος , c. 342–290 BCE. Menandros was a comic playwright who wrote 108 comedies. Popular in his own day, Menandros took first prize at the dramatic games of the Lenaia festival eight times. Many fragments and one play, almost complete, the Dyskolos , have survived the ravages of time. One quote by him is found below in the Practice Translating .
Aristarkhos of Samos, Ἀρίσταρχος ὁ Σάμιος , c. 310–c. 230 BCE. Aristarkhos was an astronomer and a mathematician who placed the sun at the center of the universe in the first known heliocentric view of the universe.
Eukleides (Euclid) of Alexandria, Εὐκλείδης c. 300 BCE. Born in Alexandria, Eukleides developed a conceptual system of geometry from a small set of axioms. His book, Elements , has been used to teach geometry up until 150 or so years ago.
Practice Translating. Translate the sentences below, taken from proverbs and a variety of ancient Greek authors. Remember the meanings and functions of the cases presented in Module 7 . Nominative case endings are bolded; genitive endings are italicized; dative endings are highlighted; and accusative endings are underlined. Note that the third declension increases the number of possible endings for the nominative singular. Check your understanding with the translations in the Answer Key . Now go back and read each sentence two or three times, noticing with each rereading how much better your understanding of the sentence becomes. Make this a habit and you will improve quickly.
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Case |
Ending |
Function |
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Nominative |
- α , - εις , - εν , - ες , - η , - ις , - ο , - οι , - ον , - ος , - υ , - υς |
predicate adjective; predicate nominative; subject of the verb |
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Genitive |
- ος , - ου |
dependence; object of adjective; object of a preposition; partitive; possession |
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Dative |
- ῃ , - οις , - ῳ |
indirect object; means or instrument |
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Accusative |
- α , - ο , - ος |
object of a preposition or verb |
- ὁ κόσμ ος ἀλλοίωσ ις · ὁ βί ος ὑπόληψ ις (Demokritos, philosopher).
- ἓν μόν ον ἀγαθ όν ἐστι· ἡ ἐπιστήμ η . καὶ ἓν μόν ον κακ όν · ἡ ἀμαθί α (Sokrates, philosopher).
- οὐδ ὲν κακ ὸν ἀμιγ ὲς καλ οῦ (Proverb).
- μέγιστ ον τόπ ος · πάντ α γὰρ χωρέει (Demokritos, philosopher).
- ἀγαθ ὸν καὶ κακ ὸν τ ὸ αὐτ ό (Herakleitos, philosopher).
- ὁ βί ος βραχ ύς · ἡ δὲ τέχν η μακρ ά · ὁ δὲ καιρ ὸς ὀξ ύς · ἡ δὲ πεῖρ α σφαλερ ή · ἡ δὲ κρίσ ις χαλεπ ή (Hippokrates, physician).
- ὁ δὲ ἀνεξέταστ ος βί ος οὐ βιωτ ὸς ἀνθρώπ ῳ (Sokrates, philosopher).
- ἐτε ῇ δὲ οὐδ ὲν ἴδμεν . ἐν βυθ ῷ γὰρ ἡ ἀλήθει α (Demokritos, philosopher)
- τ ὰ πάντ α ῥέει καὶ οὐδ ὲν μένει (Herakleitos, philosopher).
- θνητ ῶν ὄλβι ος εἰς τ ὸ τέλ ος οὐδ είς (Euripides, tragic playwright).
- πάντ ων τ ῶν ἀναγκαί ων κακ ὼν ἰατρ ὸς χρόν ος ἐστίν (Menandros, comic playwright).
- σοφώτατ ον χρόν ος · ἀνευρίσκει γὰρ πάντ α (Thales, philosopher).
- νόημ α ἢ μέτρ ον ὁ χρόν ος , οὐκ ὑπόστασ ις (Antiphon of Rhamnus, Attic orator).
- τ ὸ μέλλ ον ἄδηλ ον ἀνθρώπ οις καὶ μικρ οὶ καιρ οὶ μεγάλ ων πραγμάτ ων αἴτι οι γίγνονται (Demosthenes, Attic orator).
- τάχιστ ον νό ος · διὰ παντ ὸς γὰρ τρέχει (Thales, philosopher).
- τ ὸ τ οῦ ποδ ὸς μὲν βραδ ύ · τ ὸ τ οῦ δὲ ν οῦ ταχ ύ (Euripides, tragic playwright).
Adverbs and Verbs
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ἀνευρίσκω find out, make out, discover |
μένω remain, stay |
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* γίγνομαι be, be born |
* μόνον only |
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* εἰμί be, be possible |
ῥέω flow |
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* ζάω live |
τρέχω run |
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* ἴδμεν = ἴσμεν we know |
χωρέω make room for; retire; advance |
Adjectives, Nouns, Pronouns
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Νο minative |
Genitive |
Dative |
Accusative |
English Equivalent |
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* ἀγαθόν |
ἀγαθοῦ |
ἀγαθῷ |
ἀγαθόν |
good, noble |
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ἄδηλον |
ἀδήλου |
ἀδήλῳ |
ἄδηλον |
unclear, unseen |
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α ἴτιοι |
αἰτίων |
αἰτίοις |
αἰτί ους |
responsible, guilty |
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ἀλήθεια |
ἀληθείας |
ἀληθείᾳ |
ἀλήθειαν |
truth |
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ἀλλοίωσις |
ἀλλοιώσεως |
ἀλλοιώσει |
ἀ λλοίωσιν |
change, difference |
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ἀμαθία |
ἀμαθίας |
ἀ μαθίᾳ |
ἀμαθίαν |
ignorance |
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ἀμιγές |
ἀμιγέος (- ους ) |
ἀμιγεῖ |
ἀμιγές |
unmixed + gen. |
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ἀναγκαῖα |
ἀ ναγκαίων |
ἀναγκαίοις |
ἀναγκαῖα |
necessary, inevitable |
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ἀνεξέταστος |
ἀνεξετάστου |
ἀνεξετάστῳ |
ἀνεξέταστον |
unexamined |
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* ἄνθρωπος |
ἀνθρώπου |
ἀνθρώπῳ |
ἄνθρωπον |
human, person |
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* αὐτόν see τὸ αὐτόν the same |
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* βίος |
βίου |
βίῳ |
βίον |
life |
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βιωτός |
βιωτοῦ |
βιωτῷ |
βιωτόν |
livable, worth living |
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βραδύ |
βραδέος |
βραδεῖ |
βραδύ |
slow, dull |
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βραχύς |
βραχέος |
βραχεῖ |
βραχύν |
short, small; brief |
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βυθός |
βυθοῦ |
βυθῷ |
βυθόν |
depth, abyss |
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*ἕν |
ἑνός |
ἑνί |
ἕν |
one |
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ἐπιστήμη |
ἐπιστήμης |
ἐπιστήμῃ |
ἐπιστήμην |
knowledge; skill |
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ἐτεή |
ἐτεῆς |
ἐτεῇ |
ἐτεήν |
reality |
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θνητοί |
θνητῶν |
θνητοῖς |
θνητούς |
mortals |
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ἰατρός |
ἰατροῦ |
ἰατρῷ |
ἰατρόν |
doctor |
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* καιρός |
καιροῦ |
καιρῷ |
καιρόν |
right moment, |
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* κακόν |
κακοῦ |
κακῷ |
κακόν |
bad, evil, cowardly |
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* κακά |
κακῶν |
κακοῖς |
κακά |
bad, evil, cowardly |
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* καλόν |
καλοῦ |
καλῷ |
καλόν |
beautiful, good |
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κόσμος |
κόσμου |
κόσμῳ |
κόσμον |
ornament, dress |
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κρίσις |
κρίσεως |
κρίσει |
κρίσιν |
judgment; decision |
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μακρά |
μακρῶν |
μακροῖς |
μακρά |
long, tall |
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* μέγαλα |
μεγάλων |
μεγάλοις |
μέ γαλα |
big, great, large |
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μέγιστον |
μεγίστου |
μεγίστῷ |
μέγιστον |
greatest |
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* μέλλον see τό μέλλον the future |
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μέτρον |
μέτρου |
μέτρῳ |
μέτρον |
measure, size |
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* μικροί |
μικρῶν |
μικροῖς |
μικρούς |
small, little, short |
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νόημα |
νοήματος |
νοήματι |
νόημα |
perception, thought |
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νόος ( νοῦς ) |
νόου ( νοῦ ) |
νόῳ ( νῷ ) |
νόον ( νοῦν ) |
mind, intellect |
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ὄλβιος |
ὀλβίου |
ὀλβίῳ |
ὄλβιον |
happy, blessed |
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ὀξύς |
ὀξέος |
ὀξεῖ |
ὀξύν |
sharp, keen, swift |
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* οὐδείς |
οὐδένος |
οὐδένι |
οὐδένα |
noone |
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* οὐδέν |
οὐδένος |
οὐδένι |
οὐδέν |
nothing |
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* πάντα |
πάντων |
πᾶσι ( ν ) |
πάντα |
all, each, whole |
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πεῖρα |
πείρας |
πείρᾳ |
πεῖραν |
experience |
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πούς |
ποδός |
ποδί |
πόδα |
foot |
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* πράγματα |
πραγμάτων |
πράγμασι ( ν ) |
πρ άγματα |
matter; affair |
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σοφώτατον |
σοφωτάτου |
σοφωτάτῳ |
σοφώτατον |
wisest |
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σφαλερή |
σφαλερῆς |
σφαλερῇ |
σφαλερήν |
slippery, perilous |
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τάχιστον |
ταχίστου |
ταχίστῳ |
τάχιστον |
swiftest |
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* ταχύ |
ταχέος |
ταχεῖ |
ταχύ |
swift |
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* τέλος |
τέλεος (- ους ) |
τέλει |
τέλος |
end, power, office |
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τέχνη |
τέχνης |
τέχνῃ |
τέχνην |
skill, art |
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* τὸ αὐτό |
τοῦ αὐτοῦ |
τῷ αὐτῷ |
τὸ αὐτό |
the same |
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* τὸ μέλλον |
τοῦ μέλλοντος |
τῷ μέλλοντι |
τὸ μέλλον |
the future |
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* τόπος |
τόπου |
τόπῳ |
τόπον |
place, spot |
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ὑπόληψις |
ὑ πολήψεως |
ὑπολήψει |
ὑπόληψιν |
taking-up, continuation; reply; suspicion |
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ὑπ όστασις |
ὑποστάσεως |
ὑποστάσει |
ὑπόστασιν |
support; sediment; duration; substance |
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χαλεπή |
χαλεπῆς |
χαλεπῇ |
χαλεπήν |
difficult, harsh |
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* χρό νος |
χρόνου |
χρόνῳ |
χρόνον |
time |
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The asterisk indicates the top 250 most frequently occurring vocabulary, which you are to memorize.
Case
Ending
Function
Nominative
- α , αι , - ες , - εις , - η , - ις , - ν , - ο , - οι , - ον , - ος , - ς , - ων
predicate adjective; predicate nominative; subject of the verb
Genitive
- εος - ης , - ου , - ων
dependence; possession object of preposition
Dative
- ι , - ῳ
indirect object; means or instrument; object of the preposition or verb
Accusative
- ι , - ο , - ον , - ρ
object of the verb
- κάτοπτρ ον εἴδ εος χαλκ ός ἐστί , οἶν ος δὲ ν οῦ (Aiskhylos, tragic playwright).
- ἀνθρώπ ῳ σοφ ῷ πᾶσ α γ ῆ βατ ή · ψυχ ῆς γὰρ ἀγαθ ῆς πατρ ὶς ὁ ξύμπα ς κόσμ ος (Demokritos, philosopher).
- κακ ῆς ἀπ ’ ἀρχ ῆς γίγνεται τέλ ος κακ όν (Euripides, tragic playwright).
- διάφορ οι δὲ φύσ εις βροτ ῶν , διάφορ οι δὲ τρόπ οι (Euripides, tragic playwright).
- ὁ κόσμ ος σκην ή , ὁ βί ος πάροδ ος . ἔρχῃ , ὁράεις , ἀπέρχῃ (Demokritos, philosopher).
- τ ὸ πεπρωμέν ον φυγεῖν ἀδύνατ ον (Proverb).
- χαλεπ ὰ τ ὰ καλ ά (Proverb).
- μί α χελιδ ὼν ἔα ρ οὐ ποιέει· μί α μέλισσ α μέλ ι οὐ ποιέει (Proverb).
- τ ῷ ξέν ῳ δεῖ ἀκολουθέειν τ οῖς ἐπιχωρί οις νόμ οις (Proverb).
- ὁ φίλ ος τ ὸν φίλ ον ἐν κινδύν οις γιγνώσκει (Proverb).
- μακρ αὶ τυράνν ων χεῖρ ες (Proverb).
- εἰ πεινάεις , πᾶ ν ἐστι χρῆμ α ἐδώδιμ ον (Proverb).
- πολυμαθί η νό ον οὐ διδάσκει (Herakleitos, philosopher).
- ὁ ἄνθρωπ ος φύσε ι πολιτικ όν ζῶ ον (Aristoteles, philosopher).
- βί ος ἀνεόρταστ ος μακρ ὰ ὁδ ὸς ἀπανδόκευτ ος (Demokritos, philosopher).
- κρεῖσσ ον ἄρχεσθαι τ οῖς ἀνοήτ οις ἢ ἄρχειν (Proverb).
Adverbs and Verbs
|
ἀκολουθέω follow, accompany + dat. |
* εἰμί be |
|
ἀπέρχομαι depart |
* ἔρχομαι come, go |
|
* ἄρχω rule, command; begin + gen. |
* ὁράω see |
|
* γίγνομαι be, be born |
πεινάω be hungry |
|
* γιγνώσκω know |
* ποιέω do, make, cause; (mid.) consider |
|
* δεῖ it is necessary + ‘x’ in gen. or dat. or acc. + inf., δεῖ ἐλθε ῖν it is necessary to come |
* φυγεῖν to flee |
|
διδάσκω teach, instruct |
Adjectives, Nouns, Pronouns
|
Νοminative |
Genitive |
Dative |
Accusative |
English Equivalent |
|
ἀπανδόκευτος |
- δοκεύτου |
- δοκεύτῳ |
- δόκευτον |
without an inn |
|
* ἀγαθή |
ἀγαθῆς |
ἀγαθῇ |
ἀγαθήν |
good, noble |
|
ἀδύνατον |
ἀδυνά του |
ἀδυνάτῳ |
ἀδύνατον |
impossible |
|
ἀνεόρταστος |
ἀνεορτάστου |
ἀνεορτάστῳ |
ἀνεόρταστον |
no feasting |
|
* ἄνθρωπος |
ἀνθρώπου |
ἀνθρώπῳ |
ἄνθρωπον |
human, person |
|
ἀνό ητοι |
ἀνοήτων |
ἀνοήτοις |
ἀνοήτους |
foolish, stupid |
|
* ἀρχή |
ἀρχῆς |
ἀρχῇ |
ἀρχήν |
rule; beginning |
|
βατή |
βατῆς |
βατῇ |
βατήν |
accessible, passable |
|
* β ίος |
βίου |
βίῳ |
βίον |
life |
|
βροτοί |
βροτῶν |
βροτοῖς |
βροτούς |
mortals |
|
* γῆ |
γῆς |
γῇ |
γῆν |
land, earth |
|
διάφοροι |
διαφόρων |
διαφόροις |
διαφόρους |
unlike; differing |
|
ἔαρ |
ἔαρος |
ἔαρι |
ἔαρ |
spring |
|
ἐδώδιμον |
ἐδωδίμου |
ἐδωδίμῳ |
ἐδ ώδιμον |
edible |
|
εἶδος |
εἴδεος (- ους ) |
εἴδει |
εἶδος |
form, shape; beauty |
|
ἐπιχώριοι |
ἐπιχωρίων |
ἐπιχωρίοις |
ἐπιχωρί ους |
of the country, local |
|
ζῶον |
ζώου |
ζώῳ |
ζῶον |
animal |
|
* κακή |
κακῆς |
κακῇ |
κακήν |
bad, evil, cowardly |
|
* κακόν |
κακοῦ |
κακῷ |
κακόν |
bad, evil, cowardly |
|
* καλά |
καλῶν |
καλοῖς |
καλά |
beautiful, good |
|
κάτοπτρον |
κατόπτρου |
κατόπτρῳ |
κάτοπτρον |
mirror |
|
κίνδυνοι |
κινδύνων |
κινδύνοις |
κινδύνους |
dangers |
|
κόσμος |
κόσμου |
κόσμῳ |
κόσμον |
ornament, dress |
|
κρεῖσσον |
κρείσσονος |
κρείσσονι |
κρεῖσσον |
better |
|
μακρά (- αί ) |
μακρᾶς (- ῶν ) |
μακρᾷ (- αῖς ) |
μακράν (- άς ) |
long, tall |
|
μέλι |
μέλιτος |
μέλιτι |
μέλι |
honey |
|
μέλισσα |
μελίσσης |
μελίσσῃ |
μέλισσαν |
bee |
|
*μία |
μιᾶς |
μιᾷ |
μίαν |
one |
|
νόμοι |
νόμων |
νόμοις |
νόμους |
laws, customs |
|
νόος ( νοῦς ) |
νόου ( νοῦ ) |
νόῳ ( νῷ ) |
νόον ( νοῦν ) |
mind, intellect |
|
ξένος ( ξεῖνος ) |
ξένου |
ξένῳ |
ξένον |
stranger, guest-friend |
|
ξύμπας |
ξύμπαντος |
ξύμπαντι |
ξύμπαντα |
all, every, entire |
|
ὁδός |
ὁδοῦ |
ὁδῷ |
ὁδόν |
road, path; journey |
|
οἶνος |
οἴνου |
οἴνῳ |
οἶνον |
wine |
|
πᾶν |
παντός |
παντί |
πᾶν |
all, every, entire |
|
πᾶσα |
πάσης |
πάσῃ |
πᾶσαν |
all, every, entire |
|
πάροδος |
παρόδου |
παρόδῳ |
πάροδον |
entranceway |
|
πατρίς |
πατρίδος |
πατρίδι |
πατρίδα |
fatherland, country |
|
πεπρωμένον see τὸ πεπρωμένον fate |
||||
|
πολιτικόν |
πολιτικοῦ |
πολιτικῷ |
πολιτικόν |
of a city-state |
|
πολυμαθίη |
πολυμαθί ης |
πολυμαθίῃ |
πολυμαθίην |
great knowledge |
|
σκηνή |
σκηνῆς |
σκην ῇ |
σκηνήν |
tent; booth; stage |
|
σοφός |
σοφοῦ |
σοφῷ |
σοφ όν |
wise |
|
* τέλος |
τέλεος (- ους ) |
τέλει |
τέλος |
end, power, office |
|
τὸ πεπρωμένον |
τοῦ - μένου |
τῷ - μένῳ |
τὸ - μένον |
fate |
|
* τρ όποι |
τρόπων |
τρόποις |
τρόπους |
ways; characters |
|
τύ ραννοι |
τυράννων |
τυράννοις |
τυράννους |
tyrants |
|
* φίλος |
φίλου |
φίλῳ |
φίλον |
friend |
|
* φύσις (- εις ) |
φύσεως (- εων ) |
φύσει (- εσι ) |
φύσιν (- εις ) |
nature |
|
χαλεπά |
χαλεπῶν |
χαλεποῖς |
χαλεπά |
difficult, harsh |
|
χαλκός |
χαλκοῦ |
χαλκῷ |
χαλκόν |
copper, bronze |
|
* χεῖρες |
χειρῶν |
χερσ ί ( ν ) |
χεῖρας |
hand; force, army |
|
χελιδών |
χελιδόνος |
χελιδόνι |
χελιδόνα |
swallow |
|
* χρῆμα |
χρήματος |
χρήματι |
χρῆμα |
thing; (pl.) money |
|
* ψυχή |
ψυχῆς |
ψυχῇ |
ψυχήν |
soul |
- The asterisk indicates the top 250 most frequently occurring vocabulary, which you are to memorize.
Practice Parsing Greek Sentences. Parse each word of the sentences found below. For nouns and pronouns, give case and function. For verbs give person, number, tense, mood, and voice. For adverbs and conjunctions, identify them. For prepositional phrases give the preposition and the preposition’s object. For adjectives tell what noun they agree with in gender, number, and case.
τῷ ξ ένῷ δεῖ ἀκολουθέειν τοῖς ἐπιχωρίοις νόμοις .
τὸ τοῦ ποδὸς μὲν βραδ ύ· τὸ τοῦ δὲ νοῦ ταχύ .
Check your answers with those in the Answer Key .
Module 15 Top 250 Vocabulary to be Memorized. Like learning the alphabet and endings, memorizing vocabulary is essential to acquiring language. The better you memorize the top 250 most frequently occurring words, the greater mastery of the language you will have.
Pronoun and Nouns
------, ἀλλήλων one another, each other
ἀρχή , ἀρχῆς ἡ rule, command; beginning; province
γῆ , γῆς ἡ land, earth
γένος , γένεος ( γένους ) τό race, kind, sort; birth, origin
μήν , μηνός ὁ month ; (adv.) truly, surely
σῶμα , σώματος τό body
χώρᾱ , χώρᾱς ἡ land, country
Verb
ἡγέομαι lead; believe ; lead, command + dat.


5.1: The Principle of Mathematical Induction
The Principle of Mathematical Induction ( PMI ) may be the least intuitive proof method available to us. Indeed, at first, PMI may feel somewhat like grabbing yourself by the seat of your pants and lifting yourself into the air. Despite the indisputable fact that proofs by PMI often feel like magic, we need to convince you of the validity of this proof technique. It is one of the most important tools in your mathematical kit!
The simplest argument in favor of the validity of PMI is simply that it is axiomatic. This may seem somewhat unsatisfying, but the axioms for the natural number system, known as the Peano axioms, include one that justifies PMI. The Peano axioms will not be treated thoroughly in this book, but here they are:
- There is a least element of \(\mathbb{N}\) that we denote by \(0\).
- Every natural number a has a successor denoted by \(s(a)\). (Intuitively, think of \(s(a) = a + 1\).)
- There is no natural number whose successor is \(0\). (In other words, \(-1\) isn’t in \(\mathbb{N}\).)
- Distinct natural numbers have distinct successors. (\(a \neq b \implies s(a) \neq s(b)\))
- If a subset of the natural numbers contains \(0\) and also has the property that whenever \(a ∈ S\) it follows that \(s(a) ∈ S\), then the subset \(S\) is actually equal to \(\mathbb{N}\).
The last axiom is the one that justifies PMI. Basically, if \(0\) is in a subset, and the subset has this property about successors 1 , then \(1\) must be in it. But if \(1\) is in it, then \(1\)’s successor (\(2\)) must be in it. And so on . . .
The subset ends up having every natural number in it.
Verify that the following symbolic formulation has the same content as the version of the \(5^{\text{th}}\) Peano axiom given above.
\(∀S ⊆ N (0 ∈ S) ∧ (∀a ∈ \mathbb{N}, a ∈ S \implies s(a) ∈ S) \implies S = \mathbb{N}\)
On August \(16^{\text{th}}\) \(2003\), Ma Lihua of Beijing, China earned her place in the record books by single-handedly setting up an arrangement of dominoes standing on end (actually, the setup took \(7\) weeks and was almost ruined by some cockroaches in the Singapore Expo Hall) and toppling them. After the first domino was tipped over it took about six minutes before \(303,621\) out of the \(303,628\) dominoes had fallen. (One has to wonder what kept those other \(7\) dominoes upright . . . )
This is the model one should keep in mind when thinking about PMI: domino toppling. In setting up a line of dominoes, what do we need to do in order to ensure that they will all fall when the toppling begins? Every domino must be placed so that it will hit and topple its successor. This is exactly analogous to \((a ∈ S \implies s(a) ∈ S)\). (Think of \(S\) having the membership criterion, \(x ∈ S =\) “\(x\) will have fallen when the toppling is over.”) The other thing that has to happen (barring the action of cockroaches) is for someone to knock over the first domino. This is analogous to \(0 ∈ S\).
Rather than continuing to talk about subsets of the naturals, it will be convenient to recast our discussion in terms of infinite families of logical statements. If we have a sequence of statements, (one for each natural number) \(P_0, P_1, P_2, P_3, . . .\) we can prove them all to be true using PMI. We have to do two things. First – and this is usually the easy part – we must show that P0 is true (i.e. the first domino will get knocked over). Second, we must show, for every possible value of \(k\), \(P_k \implies P_{k+1}\) (i.e. each domino will knock down its successor). These two parts of an inductive proof are known, respectively, as the basis and the inductive step .
An outline for a proof using PMI:
\[∀n ∈ N, P_n\]
- Proof
-
(By induction)
Basis: . . . (Here we must show that \(P_0\) is true.)
Inductive step: . . . (Here we must show that \(∀k, P_k \implies P_{k+1}\) is true.)
Q.E.D.
Soon we’ll do an actual example of an inductive proof, but first we have to say something REALLY IMPORTANT about such proofs. Pay attention! This is REALLY IMPORTANT! When doing the second part of an inductive proof (the inductive step), you are proving a UCS, and if you recall how that’s done, you start by assuming the antecedent is true. But the particular UCS we’ll be dealing with is \(∀k, P_k \implies P_{k+1}\). That means that in the course of proving \(∀n\), \(P_n\) we have to assume that \(P_k\) is true. Now this sounds very much like the error known as “circular reasoning,” especially as many authors don’t even use different letters (\(n\) versus \(k\) in our outline) to distinguish the two statements. (And, quite honestly, we only introduced the variable \(k\) to assuage a certain lingering guilt regarding circular reasoning.) The sentence \(∀n\), \(P_n\) is what we’re trying to prove, but the sentence we need to prove in order to do that is \(∀k, P_k \implies P_{k+1}\). This is subtly different – in proving that \(∀k\), \(P_k \implies P_{k+1}\) (which is a UCS!) we assume that \(P_k\) is true for some particular value of \(k\).
The sentence Pk is known as the inductive hypothesis. Think about it this way: If we were doing an entirely separate proof of \(∀n\), \(P_n \implies P_{n+1}\), it would certainly be fair to use the inductive hypothesis, and once that proof was done, it would be okay to quote that result in an inductive proof of \(∀n\), \(P_n\). Thus we can compartmentalize our way out of the difficulty!
Okay, so on to an example. In Section 4.1 , we discovered a formula relating the sizes of a set \(A\) and its power set \(\mathcal{P}(A)\). If \(|A| = n\) then \(|\mathcal{P}(A)| = 2^n\). What we’ve got here is an infinite family of logical sentences, one for each value of \(n\) in the natural numbers,
\(|A| = 0 \implies |\mathcal{P}(A)| = 2^0, \\ |A| = 1 \implies |\mathcal{P}(A)| = 2^1, \\ |A| = 2 \implies |\mathcal{P}(A)| = 2^2, \\ |A| = 3 \implies |\mathcal{P}(A)| = 2^3,\)
et cetera.
This is exactly the sort of situation in which we use induction
For all finite sets \(A\),
\[|A| = n \implies |\mathcal{P}(A)| = 2^n.\]
- Proof
-
Let \(n = |A|\) and proceed by induction on \(n\).
Basis: Suppose \(A\) is a finite set and \(|A| = 0\), it follows that \(A = ∅\). The power set of \(∅\) is \(\{∅\}\) which is a set having \(1\) element. Note that \(2^0 = 1\).
Inductive step: Suppose that \(A\) is a finite set with \(|A| = k + 1\). Choose some particular element of \(A\), say \(a\), and note that we can divide the subsets of \(A\) (i.e. elements of \(\mathcal{P}(A)\)) into two categories, those that contain \(a\) and those that don’t.
Let \(S_1 = \{X ∈ \mathcal{P}(A) a ∈ X\}\) and let \(S_2 = \{X ∈ \mathcal{P}(A) a \notin X\}\). We have created two sets that contain all the elements of \(\mathcal{P}(A)\), and which are disjoint from one another. In symbolic form, \(S_1 ∪ S_2 = \mathcal{P}(A)\) and \(S_1 ∩ S_2 = ∅\). It follows that \(|\mathcal{P}(A)| = |S_1| + |S_2|\).
Notice that \(S_2\) is actually the power set of the \(k\)-element set \(A \setminus \{a\}\). By the inductive hypothesis, \(|S_2| = 2^k\). Also, notice that each set in \(S_1\) corresponds uniquely to a set in \(S_2\) if we just remove the element a from it. This shows that \(|S_1| = |S_2|\). Putting this all together we get that \(|P(A)| = 2^k + 2^k = 2(2^k) = 2^{k+1}\).
Q.E.D.
Here are a few pieces of advice about proofs by induction:
- Statements that can be proved inductively don’t always start out with \(P_0\). Sometimes \(P_1\) is the first statement in an infinite family. Sometimes it's \(P_5\). Don’t get hung up about something that could be handled by renumbering things.
- In your final write-up you only need to prove the initial case (whatever it may be) for the basis, but it is a good idea to try the first several cases while you are in the “draft” stage. This can provide insights into how to prove the inductive step, and it may also help you avoid a classic error in which the inductive approach fails essentially just because there is a gap between two of the earlier dominoes. 2
- It is a good idea to write down somewhere just what it is that needs to be proved in the inductive step — just don’t make it look like you’re assuming what needs to be shown. For instance, in the proof above it might have been nice to start the inductive step with a comment along the following lines, “What we need to show is that under the assumption that any set of size \(k\) has a power set of size \(2^k\), it follows that a set of size \(k + 1\) will have a power set of size \(2^{k+1}\).”
We’ll close this section with a short discussion about nothing.
When we first introduced the natural numbers (\(\mathbb{N}\)) in Chapter 1 we decided to follow the convention that the smallest natural number is \(1\). You may have noticed that the Peano axioms mentioned in the beginning of this section treat \(0\) as the smallest natural number. So, from here on out we are going to switch things up and side with Dr. Peano. That is, from now on we will use the convention
\(\mathbb{N} = \{0, 1, 2, 3, . . .\}\)
Hmmm. . . Maybe that was a short discussion about something after all.
Exercises:
Consider the sequence of numbers that are \(1\) greater than a multiple of \(4\). (Such numbers are of the form \(4j + 1\).)
\(1, 5, 9, 13, 17, 21, 25, 29, . . .\)
The sum of the first several numbers in this sequence can be expressed as a polynomial.
\(\sum^{n}_{j=0} 4j + 1 = 2n^2 + 3n + 1\)
Complete the following table in order to provide evidence that the formula above is correct.
| \(n\) | \(\sum^{n}_{j=0} 4j + 1\) | \(2n^2 + 3n + 1\) |
|---|---|---|
| \(0\) | \(1\) | \(1\) |
| \(1\) | \(1 + 5\) | \(2 · 1^2 + 3 · 1 + 1 = 6\) |
| \(2\) | \(1 + 5 + 9 =\) | |
| \(3\) | ||
| \(4\) |
What is wrong with the following inductive proof of “all horses are the same color.”?
Let \(H\) be a set of \(n\) horses, all horses in \(H\) are the same color.
Proof: We proceed by induction on \(n\).
Basis: Suppose \(H\) is a set containing \(1\) horse. Clearly, this horse is the same color as itself.
Inductive step: Given a set of \(k + 1\) horses \(H\) we can construct two sets of \(k\) horses. Suppose \(H = \{h_1, h_2, h_3, . . . h_{k+1}\}\). Define \(H_a = \{h_1, h_2, h_3, . . . h_k\}\) (i.e. \(H_a\) contains just the first \(k\) horses) and \(H_b = \{h_2, h_3, h_4, . . . h_{k+1}\}\) (i.e. \(H_b\) contains the last \(k\) horses). By the inductive hypothesis both these sets contain horses that are “all the same color.” Also, all the horses from \(h_2\) to \(h_k\) are in both sets so both \(H_a\) and \(H_b\) contain only horses of this (same) color. Finally, we conclude that all the horses in \(H\) are the same color.
Q.E.D.
For each of the following theorems, write the statement that must be proved for the basis – then prove it, if you can!
The sum of the first \(n\) positive integers is \(\dfrac{(n^2 + n)}{2}\).
The sum of the first \(n\) (positive) odd numbers is \(n^2\).
If \(n\) coins are flipped, the probability that all of them are “heads” is \(\dfrac{1}{2}^n\).
Every \(2^n × 2^n\) chessboard – with one square removed – can be tiled perfectly 3 by L-shaped trominoes.  There are two kinds, straight and L-shaped . This problem is only concerned with the L-shaped trominoes.)
Suppose that the rules of the game for PMI were changed so that one did the following: ˆ
- Basis: Prove that \(P(0)\) is true.
- Inductive step: Prove that for all \(k\), \(P_k\) implies \(P_{k+2}\)
Explain why this would not constitute a valid proof that \(P_n\) holds for all natural numbers \(n\). How could we change the basis in this outline to obtain a valid proof?
If we wanted to prove statements that were indexed by the integers,
\(∀z ∈ \mathbb{Z}\), \(P_z\),
what changes should be made to PMI?


7.5: Tertiary structure of proteins
- Define the tertiary structure of proteins and understand the interactions that form and maintain the tertiary structure.
What is the tertiary structure of proteins?
The secondary structure of proteins represents the folding of portions of the polypeptide held primarily by hydrogen bonding between \(\ce{C=O}\) and \(\ce{N-H}\) groups of the polymer backbone. The overall protein chain also folds in a configuration that causes more stabilizing interaction primarily between the groups on the side chains (\(\ce{-R}\)) and the between side chain groups and the groups on the polymer backbone.
The three-dimensional arrangement of all the atoms of a single polypeptide chain in space, held together by stabilizing interactions between the side chain and the backbone groups, is called the tertiary structure of proteins .
The interactions stabilizing the tertiary structure include disulfide linkage, salt bridge, coordinate bonds with metal ions, hydrogen bonding, and hydrophobic interaction, as shown in Figure \(\PageIndex{1}\). and explained below.
Disulfide linkage
When thiol (\(\ce{-SH}\)) groups of two cysteine residues come close to each other in a folded protein chain, they can make disulfide linkage ((\(\ce{-S-S{-}}\)), i.e., the only covalent bond, besides peptide bond, holding amino acid residues together in proteins.
\(\ce{R-SH + HS-R' ->[Oxidation] R-S-S-R + 2H^{+} + 2e^{-}}\)
Salt bridge
The side chain of acidic amino acids, e.g., Asp, loses protons and becomes an anion, and that of basic amino acids, e.g., Lys, gains a proton and becomes a cation. When the opposite ions come close to each other, they make an ionic bond, like that in salts, called salt-bridge, e.g., \(\ce{...-CH2-COO^{-} ^{+}NH3-(CH2)4-...}\)) can form between Asp and Lys residues. This is an ionic bond holding opposite charges together.
Coordinate bond
Some metals can act as Lewis acids and make a coordinate covalent bond by accepting a lone pair of electrons from Lewis bases. Oxygen and nitrogen atoms in proteins have lone pairs of electrons and can act as Lewis bases. For example, oxygen atoms of two carboxylate \(\ce{-COO^{-}}\) groups can make coordinate covalent bonds with \(\ce{Mg^{2+}}\), resulting in a coordinate covalent linkage (\(\ce{-COO^{-}\!\!\!\!\!->\!\!Mg^{2+}\!\!\!\!\!\!\!\!<-\!\!\!\!\! ^{-}OOC{-}}\)) between the amino acid residues.
Hydrogen bonding
Hydrogen atoms bonded to oxygen or nitrogen atoms, e.g., in \(\ce{-OH}\) and \(\ce{-NH2}\), can make hydrogen bonds with any oxygen or nitrogen atom. These bonds could be between side chains, backbone groups, or side chains and backbone groups. For example, \(\ce{-OH}\) in the side chain of serine can make hydrogen with the carbonyl oxygen of the amide group (\(\ce{-CONH2}\)) of asparagine residue, as shown below.
Hydrophobic interactions
As shown below, amino acids with aliphatic or aromatic hydrophobic side chains, e.g., valine and phenylalanine, establish hydrophobic interaction.
Hydrophobic interaction is London dispersion forces between nonpolar groups. The physiological medium is predominantly water. As a nonpolar liquid like oil, when mixed with a polar liquid like water, the oil drops merge, expelling water. Similarly, hydrophobic groups in proteins come close to each other due to the hydrophobic interaction and tend to stay in the interior of the protein, expelling water away from those regions. Ionic and polar compounds dissolve in water. Similarly, ionic and polar groups on the side chains stay on the proteins' outer surfaces, interacting more with water.
The tertiary structure of proteins may be predominantly \(\alpha\)-helix, \(\beta\)-pleated sheets, or random coil, but often it is a mix of these, for example, Carboxypeptidase A from bovine pancreas, shown in Figure \(\PageIndex{2}\).


11.12: Large Intestine
The large intestine consists of the caecum , colon and rectum . The chyme from the small intestine that enters the colon consists mainly of water and undigested material such as cellulose (fibre or roughage). In omnivores like the pig and humans the main function of the colon is absorption of water to give solid faeces. Bacteria in this part of the gut produce vitamins B and K.
The caecum, which forms a dead-end pouch where the small intestine joins the large intestine, is small in pigs and humans and helps water absorption. However, in rabbits, rodents and horses, the caecum is very large and called the functional caecum . It is here that cellulose is digested by micro-organisms. The appendix , a narrow dead end tube at the end of the caecum, is particularly large in primates but seems to have no digestive function.


9.5: Sample Documentation
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The patient denies abdominal pain, nausea, vomiting, bloating, constipation, diarrhea, urinary pain, urgency or frequency, change in appetite, food intolerance, dysphagia, or personal or family history. Abdominal contour is flat and symmetric. No visible lesions, pulsations, or peristalsis noted. Bowel sounds present and normoactive. Patient denies pain with palpation; no masses noted.
The patient reports generalized abdominal pain, along with nausea and vomiting for the last two days. Abdomen is slightly distended. Bowel sounds hypoactive in all four quadrants. Pain reported at 7/10 and guarding noted with palpation of the RLQ. Dr. Smith notified at 0730.


1.1: Solubility
Solution
The solution is a homogeneous mixture of two or more substances.
- Miscible substances make a solution upon mixing in any proportion. For example, ethanol and water are miscible to each other.
- Immiscible substances do not make solutions upon mixing in any proportion.
- Partially miscible substances can make a solution upon mixing up to a certain extent but not in all proportions.
- A solvent is a larger substance in the solution.
- A solute is a small amount of a substance in the solution.
- An unsaturated solution is one in which the solvent holds solute less than the maximum limit, i.e., more solute can be dissolved.
- A saturated solution is one in which the solvent holds the maximum amount of solute it can dissolve.
Water -a universal solvent
Water is one of the most important solvents because it is present all around us -it covers more than 70% of the earth and more than 60% of our body mass. Water is a polar molecule having a partially negative end on oxygen and a partially positive end on hydrogen atoms. that can dissolve most of the polar and ionic compounds. In ionic compounds, cations are held by anions through electrostatic interaction. When an ionic compound dissolves into water, it dissociates into cations and anions, each surrounded by a layer of water molecules held by ion-dipole interactions. The water molecules around ions make ion-dipole interaction by orienting their partial negative end towards cations and their partial positive end towards anions. The energy needed to break ion-ion interaction in the ionic compounds is partially compensated by the energy released by establishing the ion-dipole interactions. The energy gained due to ion-dipole interactions, and nature's tendency to disperse is the driving forces responsible for the dissolution of ionic compounds.
Solubility is the ability of a substance to form a solution with another substance.
The solubility of a solute in a specific solvent is quantitatively expressed as the concentration of the solute in the saturated solution. Usually, the solubility is tabulated in the units of grams of solute per 100 mL of solvent (g/100 mL). The solubility of ionic compounds in water varies over a wide range. All ionic compounds dissolve to some extent.
For practical purposes, a substance is considered insoluble when its solubility is less than 0.1 g per 100 mL of solvent.
For example, lead(II)iodide ( \(\ce{PbI2}\) ) and silver chloride ( \(\ce{AgCl}\) ) are insoluble in water because the solubility of \(\ce{PbI2}\) is 0.0016 mol/L of the solution and the solubility of \(\ce{AgCl}\) is about 1.3 x 10 -5 mol/L of solution. Potassium iodide (\(\ce{KI}\)) and \(\ce{Pb(NO3)2}\) are soluble in water. When aqueous solutions of \(\ce{KI}\) and \(\ce{Pb(NO3)2}\) are mixed, the insoluble combination of ions, i.e., \(\ce{PbI2}\) in this case, precipitates, as illustrated in Figure \(\PageIndex{1}\).
Solubility guidelines for dissolution of ionic compounds in water
There are no fail-proof guidelines for predicting the solubility of ionic compounds in water. However, the following guidelines can predict the solubility of most ionic compounds.
- Salts of alkali metals (\(\ce{Li^+}\), \(\ce{Na^+}\), \(\ce{K^+}\), \(\ce{Rb^+}\), \(\ce{Cs^+}\)) and ammonia (\(\ce{NH4^+}\)) are soluble. For example, \(\ce{NaCl}\), and \(\ce{(NH4)3PO3}\) are soluble.
- Salts of nitrate ( \(\ce{NO3^-}\)), acetate ( \(\ce{CH3COO^-}\)), and perchlorate ( \(\ce{ClO4^-}\)) are soluble. For example, \(\ce{Pb(NO3)2}\), and \(\ce{Ca(CH3COO)2}\) are soluble.
- Salts of chloride (\(\ce{Cl^-}\)), bromide (\(\ce{Br^-}\)), and Iodide (\(\ce{I^-}\)) are soluble, except when the cation is Lead (\(\ce{Pb^{2+}}\)), Mercury (\(\ce{Hg2^{2+}}\)), or Silver (\(\ce{Ag^{+}}\)). Remember the acronym “LMS” based on the first letter of the element name or phrase ‘Let Me See” to recall Lead, Mercury, and Silver.
- Sulfates (\(\ce{SO4^{2-}}\)) are soluble except when the cation is, \(\ce{Pb^{2+}}\), \(\ce{Hg2^{2+}}\), or \(\ce{Ag^{+}}\) (recall “Let Me See” for Lead, Mercury, and Silver) or a heavy alkaline earth metal ion: calcium (\(\ce{Ca^{2+}}\)), barium (\(\ce{Ba^{2+}}\)), or strontium (\(\ce{Sr^{2+}}\)). (Remember the acronym “CBS” based on the first letter of the element name, or phrase “Come By Soon” to recall calcium, barium, and strontium.)
- Hydroxide (\(\ce{OH^{-}}\)) and sulfides (\(\ce{S^{2-}}\)) are insoluble except when the cation is a heavy alkaline earth metal ion: \(\ce{Ca^{2+}}\),\(\ce{Ba^{2+}}\), or \(\ce{Sr^{2+}}\) (recall “Come By Soon” for calcium, barium, and strontium), alkali metals and ammonium. For example, \(\ce{Mg(OH)2}\) and \(\ce{CuS}\) are insoluble.
- Carbonates (\(\ce{CO3^{2-}}\)), phosphates (\(\ce{PO4^{3-}}\)), and oxide (\(\ce{O^{2-}}\)) are insoluble except when the cation is an alkali metal ion or ammonium. For example, \(\ce{CaCO3}\), and \(\ce{Fe2O3}\) are insoluble.
- If there is a conflict between the two guidelines, the first listed guideline has priority. For example, \(\ce{CaCO3}\) is insoluble (rule#6), but \(\ce{Na2CO3}\) is soluble (rule#1 has priority over rule#6).
Precipitation reactions
Precipitation reactions are a class of chemical reactions in which two solutions are mixed, and a solid product, called a precipitate, separates out. Precipitation reaction happening upon mixing solutions of ionic compounds in water can be predicted as illustrated in Figure \(\PageIndex{2}\). The first step is to list the soluble ionic compounds and then cross-combine the cations of one with the anion of the other to make the potential products. If any of the potential products are insoluble ionic compounds, they will precipitate out. For example, when \(\ce{NaOH}\) solution is mixed with \(\ce{MgCl2}\) solution, \(\ce{Mg(OH)2}\) is a cross-combination that forms an insoluble compound, it will precipitate out.
Figure \(\PageIndex{3}\) shows precipitates of some insoluble ionic compounds formed by mixing aqueous solutions of appropriate soluble ionic compounds.


10.1: Reducing Material Variances
Learning Outcomes
- Discuss strategies to limit and reduce material variances
Ben and Mary want to get Ray in the room so they can hash this out. You are the manager and need to get to the bottom of this issue with the material variances.
Most companies create practical material quantity standards, that allow for scrap, spoilage, inefficiencies and rejected material. The situations we have discussed go outside of what is already built in to our budget.
Example
So back to Ben, Mary, and Ray. You, as the manager, need to sit down with these three and get this problem figured out. Let’s strategize ways to get closer to our budgeted material quantities.
- Ben might want to compare the quality of a previous batch of raw materials against the newer batches. Maybe it is a quality issue that needs to be addressed with the supplier. If this is the case, Ben and Mary can work together with the production staff who use the product to outline the problems. Perhaps Ben could get a discount on the raw materials if it was in fact, a lower quality, to help offset the additional costs incurred by the company.
- Mary can review procedures with the production staff. Mary may need to set some standard procedures, so all employees are doing things in the same way. She may need to spend time on the floor, watching the machines and people work, and noting areas of inefficiency. It might be good to get Ray in on this process as well, just in case there are equipment issues that need to be fixed.
- Invest in newer or better equipment. This may be an option, if analysis shows that the efficiency of the new equipment will improve processes, reduce material or labor usage, improving the production process overall.
- Once the potential issues are identified, bring everyone together to discuss the findings, and determine if the material quantities budgeted are accurate, or need to be modified.
Good systems in place from budgeting to purchasing to production are necessary to insure the best quality product is produced at the lowest cost.
Learn More
For another example, take a look at THIS ARTICLE .  Whether you are buying a $1 component or $100 per pound product, saving money on raw materials will help to improve the bottom line, as long as the quality is good and waste is minimized.
Practice Questions


8: Cell Division by Mitosis
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- 8.1: Introduction
- A human, as well as every sexually reproducing organism, begins life as a fertilized egg (embryo) or zygote. Trillions of cell divisions subsequently occur in a controlled manner to produce a complex, multicellular human. In other words, that original single cell is the ancestor of every other cell in the body. Once a being is fully grown, cell reproduction is still necessary to repair or regenerate tissues.
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- 8.2: Cell Division
- The continuity of life from one cell to another has its foundation in the reproduction of cells by way of the cell cycle. The cell cycle is an orderly sequence of events that describes the stages of a cell’s life from the division of a single parent cell to the production of two new daughter cells. The mechanisms involved in the cell cycle are highly regulated.
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- 8.3: The Cell Cycle
- The cell cycle is an ordered series of events involving cell growth and cell division that produces two new daughter cells. Cells on the path to cell division proceed through a series of precisely timed and carefully regulated stages of growth, DNA replication, and division that produces two identical (clone) cells. The cell cycle has two major phases: interphase and the mitotic phase.
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- 8.4: Control of the Cell Cycle
- The length of the cell cycle is highly variable, even within the cells of a single organism. In humans, the frequency of cell turnover ranges from a few hours in early embryonic development, to an average of two to five days for epithelial cells, and to an entire human lifetime spent in G0 by specialized cells, such as cortical neurons or cardiac muscle cells. There is also variation in the time that a cell spends in each phase of the cell cycle.
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- 8.5: Cancer and the Cell Cycle
- Cancer is the result of unchecked cell division caused by a breakdown of the mechanisms that regulate the cell cycle. The loss of control begins with a change in the DNA sequence of a gene that codes for one of the regulatory molecules. Faulty instructions lead to a protein that does not function as it should. Any disruption of the monitoring system can allow other mistakes to be passed on to the daughter cells. Each successive cell division will give rise to daughter cells with even more damage
Thumbnail: Xenopus laevis egg imaged at 119 min post fertilization at the 4-cell stage stained for tubulin (green). (Public Domain; Martin Wuehr, Timothy Mitchison, via Cell Image Library )


5.1: Introduction
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Learning Outcomes
For every personal computer in a developing country there are roughly four mobile phones. Although many of these are likely to be older or low-end models, today’s high-end devices have the equivalent processing power of a personal computer from the mid-1990s. In comparison, personal computers today have more number crunching ability than all the computers that took the Apollo rocket to the moon 25 years earlier. The boundary between mobile phones, handheld game consoles, entertainment devices and personal computers is becoming increasingly blurred, with devices such as the Blackberry, Symbian-driven smartphones, GPS-enabled mobile phones, Ultra Mobile PCs, and Nokia’s N-Gage breaking new ground. Technology continues to advance at a remarkable pace, opening up new opportunities few people would have considered a few short years ago.


2.13: The Electrooculogram
Eye movements can be recorded using electrodes placed on the skin near the eyes. This kind of recording is an electrooculogram or EOG. An EOG records eye movement because of a voltage difference between the cornea and the retina (Figure 1). As the eye moves, the vector of this electric field changes with respect to recording electrodes placed on the skin at fixed points.
The human eye has six muscles attached to its exterior surface. These muscles are grouped into three antagonistic pairs that control horizontal, vertical, and torsional movement and position of the eye:
Horizontal axis:
- the medial rectus muscle turns the eye toward the nose (medially) (adducts)
- the lateral rectus muscle turns the eye away from nose (laterally) (abducts)
Vertical axis:
- the superior rectus muscle turns the eye up (elevates) with a slight rotation toward the nose (medially) (adducts)
- the inferior rectus muscle turns the eye down (depresses) with a slight rotation towards the nose (medially) (adducts)
Torsional axis:
- the superior oblique muscle rotates the top of the eye toward the nose (laterally) (abducts) with a slight depression
- the inferior oblique muscle rotates the top of the eye away from the nose (laterally) (abducts) with a slight elevation
These muscles are innervated by motor neurons that have electrical activity with a tonic component that controls the position of the eye, and a phasic component that controls the velocity of eye movement. Even though the eye position commands and the eye velocity commands are linear functions of the firing frequency of the motor neuron, they are separate sets of commands. The eye velocity commands are sent along a direct path from specialized brain formations or fields to the motor neurons. However, the eye position commands are the products of the integration of eye velocity commands sent along an indirect path to a network of neurons that functions as a neural integrator. It is the output of the integrator that provides eye position commands to the motor neurons.
The integration of signals from different groups of neurons in the oculomotor system control five types of eye movement, each with a unique function and distinctive properties. These types are: saccades, pursuit, vestibular ocular reflex (VOR), vergence, and optokinetic reflex.
In this experiment, the subject will perform tasks that will generate electrical activity that will alter the standing voltage between the front and back of the eye that is correlated with horizontal eyeball movement. This movement will be obtained by electrodes placed on the skin near the eye. The record of this electrical activity is known as an electrooculogram (EOG).
These electrical changes are unique to each of four different types of eye movement (saccades, VOR, pursuit, and vergence). In our experiment, we will explore saccades, vestibular ocular reflex (VOR) and pursuit.
Saccades
The fovea centralis (focal point) is the region of the retina that sees in detail. Saccadic eye movements rotate both eyes so that image of interest falls on the fovea. You are using saccades at this very moment to point the fovea of your eyes at the words in this sentence. To compensate for the poor vision that occurs during saccades, saccadic movements are quick, with a velocity from 400 degrees to as high as 800 degrees of movement in a second.
Saccades are also accurate because the saccadic system uses an internal estimate of eye position from its neural integrator to guide and stop the saccades. When looking at an object, saccades move the eye in all potential directions in the orbit, but they are interspersed with pauses in eye movement, called fixations (see the trace of eye movement in Figure 2). During fixations, the gaze is directed to a single location, only. In Figure 2, saccadic eye movement results in eye movements that allow the subject to view the different components of the picture, while fixations allow the subject to stop eye movement and focus on a single detailed feature of the picture.
Vestibular Ocular Reflex (VOR)
The vestibular ocular reflex keeps the image of the outside world stationary on the entire retina when the head moves. VOR connects lateral movement of the head in one direction with lateral movement of the eyes in the opposite direction. For example, if you rotate your head to the right as you look at this word, your eyes rotate to the left. VOR is a phasic response that is faster than pursuit because it is a simple central reflex arc that involves only three neurons. The signal that indicates the velocity of head movement originates in the semicircular canals of the ear and goes through an afferent nerve and an interneuron on its way to the motor neurons of the oculomotor muscles. The muscles rotate the eyes at a velocity that matches the velocity of the head, thus, keeping the image stationary on the retina.
The eyes are held on the image through a tonic response along an indirect path through a reverberating neural circuit between the afferent nerve and motor neurons. Without this neural circuit, which is a short-term memory device, the eyes would drift back to center and off the image while the head was still rotated.
Smooth Pursuit Eye Movements
Pursuit eye movement keeps the fovea pointed at a moving target, like a ball rolling on the horizon. Smooth pursuit movements may be vertical or horizontal, and each will produce a different pattern on the EOG. There is an initial delay (latency) in pursuit movement because the signal from the eye, that indicates the object is moving, has to be conducted through many synapses to the brainstem. Initially, when the object starts to move, a saccade helps the fovea catch up to the object until the pursuit movement begins to track the object. Smooth pursuit movements continuously track the moving target through eye movement, only (no head movement). Smooth pursuit movements are slow (up to 30 degrees per minute) and do not require fixations for focusing.
Methods
Set up
Start the Software
- Click on LabScribe3, Click Settings→ Human Muscle→ EOG
- All Students will be a subject in this experiment. Select the first person from your group to be the subject in this experiment.
- Use an alcohol swab to clean and scrub the areas where the electrodes will be placed (Methods Figure 1). Let the areas dry before attaching the electrodes.
- Trim the electrodes and then remove the plastic disk. Apply the electrodes to one of the scrubbed areas. Attach an electrode to each of the other areas.
- Attach the electrodes so that the red lead is located next to the left eye, the black lead is located next to the right eye, and the green ground is located under the right ear on/near the mastoid process.
- Electrode pads can be cut to avoid the hairline lateral to each eye and the hair line in the mastoid process area.
- Drape the leads for the electrodes and have the subject place the iWire electrode box on their lap. There should be no tension on the electrodes.
- The subject should sit quietly with their hands and iWire box on their lap.
Week 12: Electrooculogram Activity (EOG)
Note: for these activities, it is important to observe your subject’s physical eye movements.
Exercise 1: Saccades
Aim: To demonstrate the type of electrical activity that occurs in the muscles as the subject is reading using paragraphs in different settings.
The number of words in each line, the length of each line, and the formatting of the paragraph will affect the shape of the EOG recording.
Control:
- Once the electrode pads and leads are placed
- Subject will close their eyes and move their eyes left to right 4 times, and up and down 4 times and blink your eyes 4times while being recorded. This will provide a baseline and proof that electrodes are in the correct positions.
- Type in Mark box subject’s name, control, once you start Recording, click on Mark to place wording on data screen.
Narrow Normal Saccades
- Procedure for Narrow Normal Paragraph. Select writing sample #4 Narrow Normal Paragraph for the subject to read as his or her EOG is recording.
- The subject should avoid any voluntary movements of his or her head or body during the recording. ALL READING ARE TO BE DONE SILENTLY WITHOUT MOVING ANY FACIAL MUSCLES. Only the subject’s eyes should be moving while he or she is reading. Have subject hold the document at eye level.
- Type “ Narrow Normal Saccades ” in the Mark box to the right of the Mark button on the LabScribe3 Main window.
- As the subject is focusing on the first word in the paragraph, click Record . Instruct the subject to begin reading as you click on the Mark button to mark the recording.
- After the first cyclic pattern in completed, click on the AutoScale button. Observe the subject’s eyes as he or she is reading.
- Click Stop to halt recording when the subject has finished reading.
- Select Save As in the File menu, type Narrow Normal Paragraph and the subject’s name for the file. Click on the Save button to save the data file to Desktop to your Table’s Folder if desired.
Wide Normal Saccades
- Procedure for Wide Normal Paragraph. Select writing sample #11.
- The subject should avoid any voluntary movements of his or her head or body during the recording. Only the subject’s eyes should be moving while he or she is reading. Have subject hold the document at eye level.
- Type “ Wide Normal Saccades ” in the Mark box to the right of the Mark button on the LabScribe3 Main window. As the subject is focusing on the first word in the paragraph, click Record . Click the mark button to mark the start of the reading.
- Click stop and save the recording.
Wide Slow Saccades
- Type Wide Slow Saccades in the Mark box to the right of the Mark button on the LabScribe3 Main window.
- Instruct the same subject: hold the document at eye level and move from word to word in the same paragraph using a slower saccadic movement. FOCUS on each word FOR TWO SECONDS , to do this say the word to yourself twice before moving to the next word. (Example: A,A, neurologist, neurologist, has, has, etc….)
- Record, mark and save the recording: Save as Narrow Slow Saccade and the subject’s name.
Repeat these same instructions, slowly reading and focusing on each word, for the Spaced Word paragraph (words space far apart in the document), the four skeleton document (each line having the word “skeleton” spaced throughout a line four times, and the five skeleton document (each line having the word “skeleton” space throughout five times).
Exercise 2: Vestibular Ocular Reflex (VOR)
Aim: To demonstrate the type of electrical activity that occurs in the muscles as the subject remains focused on an image or word on a page while rotating his or her head from side to side.
Note: Observe the subject’s eye movements as well as the pattern of the recording.
- Using the Card with VOR printed on it, have the subject focus on the letters VOR as the subject rotates his or her head from side to side.
- Inform the subject to avoid any voluntary movements of his or her BODY during the recording . Only the subject’s HEAD should be moving while he or she is focusing on the VOR card.
- Type “VOR” in the Mark box to the right of the Mark button on the LabScribe3 Main window.
- As the subject is focusing on the VOR image and begins rotating his or her head first to the left side then to the right side . Continue moving head left to right while keeping their eyes focused on the VOR image. Click Record . Click on the Mark button to mark the recording . Have the subject do this for 15 seconds.
- After the first cyclic EOG pattern in completed: click on the AutoScale button and observe the subject’s eyes as the subject is rotating his or her head.
- When the subject has finished the exercise Click Stop .
- Select Save in the File menu.
Exercise 3: Pursuit Eye Movement
Aim: To demonstrate the type of electrical activity that occurs in the muscles as the subject follows a moving target vs a stationary target.
Use computers to view the computer-generated image of a moving ball:
For Horizontal Smooth Pursuit Test find the file named “Horizontal Ball” located on the P: drive.
- The subject must position their face 12 INCHES in front of the screen, prepare subject to focus on the LEFT SIDE of the computer screen to begin this exercise. Remind the subject that only their eyes will move in this exercise. You will record activity for Four Cycles , a Cycle is watching the dot from the LEFT to RIGHT and BACK TO LEFT . Do this Four Times.
- Type “ Horizontal Smooth Pursuit ” in the Mark box to the right of the Mark button. As the computer program is started, watch the screen and say “RECORDING” when the dots returns to the VERY LEFT HAND SIDE OF THE SCREEN and the subject begins following the target with his or her eyes.
- CLICK RECORD and Click MARK to place the Mark on the recording screen.
- REMIND the Subject that ONLY the SUBJECT’S EYES should be moving while he or she is following the target.
- Have subject follow the dot “ LEFT to RIGHT and BACK TO LEFT ” for FOUR CYCLES
After the first cyclic EOG pattern in completed,
- Click on the AutoScale button
- Observe the subject’s eyes as the subject is following the target.
6. When the target has completed FOUR CYCLES. Click STOP to halt recording Select Save in Your Table’s File on the Desktop. Title this “Horizontal Smooth Pursuit and the subject’s name.
Vertical Smooth Pursuit
For Vertical Smooth Pursuit Test find the file named “Vertical Ball” located on the P: drive.
Have COMPUTER UNPLUGED and SET AT EYE LEVEL and 12 INCHES in front of subject prepare subject to focus on the CENTER of the computer screen to begin this exercise. Remind the subject that only their eyes will move in this exercise. You will record activity for Four Cycles , a Cycle is watching the dot from the TOP TO BOTTOM BACK TO TOP. Do this Four Times.
- Type “ Vertical Smooth Pursuit ” in the Mark box to the right of the Mark button.
- As the computer program is started, watch the screen and say “RECORDING” when the dots returns to the VERY TOP OF THE SCREEN and the subject begins following the target with his or her eyes.
- CLICK RECORD and Click MARK to place the Mark on the recording screen.
- REMIND the Subject that ONLY the SUBJECT’S EYES should be moving while he or she is following the target.
- Have subject follow the dot “ TOP TO BOTTOM BACK TO TOP ” for FOUR CYCLES
After the first cyclic EOG pattern is completed,
- Click on the AutoScale button
- Observe the subject’s eyes as the subject is following the target.
6. When the target has completed FOUR CYCLES. Click STOP to halt recording Select Save in Your Table’s File on the Desktop. Title this “Vertical Smooth Pursuit and the subject’s name.